The Fluorite Structure

The general formula of crystals with the fluorite structure is MAS. The mineral fluorite, calcium fluoride, CaF2, which names the group, is sometimes also called fluorspar. 

The fluoride ion. There are two tetrahedral sites per closest-packed ion. If all the tetrahedral sites are occupied, the formula must be either MX2 or M2X. Normally, we expect the anion to be closest packed because generally anions are larger than the cations. In the case of Cap2 the fluoride ion, with an ionic radius of 1.33 A, is larger than the calcium ion (r = 1.00 A), but the structure can be analyzed by assuming that the Ca ions are closest-packed. Thus, in the illustration above (and in those below), the lighter spheres are F and the black spheres are Ca.  

Remember that cubic closest packing occurs with the ABC sequence. 

4/m32/m. If you have trouble seeing the diagonal rotoinversion axes, you might want to examine the diagonal view below, tilted just slightly to the left of one of the axes. 

rotation of 120° around the diagonal, followed by inversion through the center of symmetry, wonld produce an equivalent image (you may need a model to fully appreciate this). 

Before we leave this beautifully symmetric species, can you determine the coordination number of the cation and anion  

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The Fluorite Structure.—In Table XI are given the observed interatomic distances in crystals with the fluorite structure. There is good... 

We have accordingly shown that for values of the ratio of the crystal radius of the cation to that of the anion greater than 0.65 the fluorite structure is stable for values less than 0.65 the rutile structure is stable. 

Goldschmidt predicted from his empirical rule that calcium chloride would not have the fluorite structure, and he states that on investigation he has actually found it not to crystallize in the cubic system. Our theoretical deduction of the transition radius ratio allows us to predict that of the halides of magnesium, calcium, strontium and barium only calcium fluoride, strontium fluoride and chloride, and barium fluoride, chloride,... 

Many complex ions, such as NH4+, N(CH3)4+, PtCle", Cr(H20)3+++, etc., are roughly spherical in shape, so that they may be treated as a first approximation as spherical. Crystal radii can then be derived for them from measured inter-atomic distances although, in general, on account of the lack of complete spherical symmetry radii obtained for a given ion from crystals with different structures may show some variation. Moreover, our treatment of the relative stabilities of different structures may also be applied to complex ion crystals thus the compounds K2SnCle, Ni(NH3)3Cl2 and [N(CH3)4]2PtCl3, for example, have the fluorite structure, with the monatomic ions replaced by complex ions and, as shown in Table XVII, their radius ratios fulfil the fluorite requirement. Doubtless in many cases, however, the crystal structure is determined by the shapes of the complex ions. 

The theoretical result is derived that ionic compounds MXS will crystallize with the fluorite structure if the radius ratio Rm/Rx is greater than 0.65, and with the rutile (or anatase) structure if it is less. This result is experimentally substantiated. 

Anion Interstitials The other mechanism by which a cation of higher charge may substitute for one of lower charge creates interstitial anions. This mechanism appears to be favored by the fluorite structure in certain cases. For example, calcium fluoride can dissolve small amounts of yttrium fluoride. The total number of cations remains constant with Ca +, ions disordered over the calcium sites. To retain electroneutrality, fluoride interstitials are created to give the solid solution formula... 

Figure 1 Computer-generated schematic drawn to scale showing the fluorite structure of pure Ce02 (A), and the vacancies present in the doped Ce0 9W0 iOy reservoirs when fully charged (B) and after releasing 30% of its oxygen atoms (C).

FIGURE 7.5 The calcium fluoride structure (also known as the fluorite structure). 

The fluorite structure is a common one for compounds that have 1 2 stoichiometry. A great many compounds have formulas that have twice as many cations as anions. Examples include compounds such as Li20 and Na2S. These compounds have crystal structures that are like the fluorite structure but with the roles of the cations and anions reversed. This structure is known as the antifluorite structure, in which there are eight cations surrounding each anion and four anions surrounding each cation. The antifluorite structure is the most common one for compounds that have formulas containing twice as many cations as anions. 

Although CaF2 has the fluorite structure, MgF2 has the rutile structure. Explain this difference. 

Four solid oxide electrolyte systems have been studied in detail and used as oxygen sensors. These are based on the oxides zirconia, thoria, ceria and bismuth oxide. In all of these oxides a high oxide ion conductivity could be obtained by the dissolution of aliovalent cations, accompanied by the introduction of oxide ion vacancies. The addition of CaO or Y2O3 to zirconia not only increases the electrical conductivity, but also stabilizes the fluorite structure, which is unstable with respect to the tetragonal structure at temperatures below 1660 K. The tetragonal structure transforms to the low temperature monoclinic structure below about 1400 K and it is because of this transformation that the pure oxide is mechanically unstable, and usually shatters on cooling. The addition of CaO stabilizes the fluorite structure at all temperatures, and because this removes the mechanical instability the material is described as stabilized zirconia (Figure 7.2). 

The favored defect type in strontium fluoride, which adopts the fluorite structure, are Frenkel defects on the anion sublattice. The enthalpy of formation of an anion Frenkel defect is estimated to be 167.88 kJ mol-1. Calculate the number of F- interstitials and vacancies due to anion Frenkel defects per cubic meter in SrF2 at 1000°C. The unit cell is cubic, with a cell edge of 0.57996 nm and contains four formula units of SrF2. It is reasonable to assume that the number of suitable interstitial sites is half that of the number of anion sites. 

Sketch an edge dislocation formed by the insertion of extra material parallel to a cube edge in fluorite, CaF2, and use the FS/RH convention to determine the Burgers vector. (The fluorite structure is given in Supplementary Material SI and drawn in Fig. 4.7a.)... 

Uranium oxides are of importance in the nuclear industry, and for this reason considerable effort has been put into understanding their nonstoichiometric behavior. The dioxide, U02 crystallizes with the fluorite structure with an ideal composition MX2 (Fig. 4.7a) but is readily prepared in an oxygen-rich form. In this state it is... 

At temperatures above 1100°C uranium dioxide can exist between the composition limits of UO2 and approximately U02.25- The fluorite structure of the parent UO2 can be imagined to be constructed of edge-shared UOg cubes (Fig. 4.7b and 4.7c). At the simplest level, the composition variation can be considered to be due to the presence of interstitial anions. Each cube containing a U ion is adjacent to an empty cube. The incorporation of anions, O2-, within these empty cubes is therefore possible, and it is these interstitial positions that are occupied in oxygen-rich U02, . 

Figure 4.9 Clusters in the fluorite structure (a, b) transformation of a cube into a square antiprism (c, d) transformation of a cube into a cuboctahedron (e) a single square antiprism formed by tbe creation of < 110> interstitial defects (/) an M6F36 cluster in a fluorite structure matrix. Cations in the plane of tbe section are represented by smaller spheres anions above and below the plane are represented by larger spheres.

Figure 4.12 Coordination defects in the fluorite structure (a) fluorite structure represented as two interpenetrating sets of XM4 tetrahedra pointing along the cube < 111 > directions (b) fragment of one subset of tetrahedra, all pointing in the same direction and (c) coordination defect. The central part of the defect, heavy outline, is the unoccupied tetrahedron core of the cluster. The cubic unit cell in (a) and (b) is outlined.

A number of oxides with the fluorite structure are used in solid-state electrochemical systems. They have formulas A02 xCaO or A02 xM203, where A is typically Zr, Hf, and Th, and M is usually La, Sm, Y, Yb, or Sc. Calcia-stabilized zirconia, ZrC)2.xCaO, typifies the group. The technological importance of these materials lies in the fact that they are fast ion conductors for oxygen ions at moderate temperatures and are stable to high temperatures. This property is enhanced by the fact that there is negligible cation diffusion or electronic conductivity in these materials, which makes them ideal for use in a diverse variety of batteries and sensors. 

The parent phase is a stoichiometric oxide M02 with the fluorite structure. Substitution of a lower valence cation for Zr4+ is compensated by oxygen vacancies (Section 1.11.6 and Section 4.4.5). Taking calcia-stabilized zirconia as an example, addition of CaO drops the metal to oxygen ratio to below 2.0, and the formula of the oxide becomes Ca Zrj -x02-x. 

Another important structure is the fluorite structure exhibited by oxides with the formula M02. The coordination of the cation/anion is 8 4. The fluorite structure shown in Figure 2.2d consists of a cubic close-packed array of cations in which all the tetrahedral sites are occupied by anions. The fluorite structure corresponding to the mineral CaF2 is exhibited in oxides such as ZrOz, HfD2, U02, and Tb02. 

Anion conduction, particularly oxide and fluoride ion conduction, is found in materials with the fluorite structure. Examples are Cap2 and Zr02 which, when doped with aliovalent impurities. Fig. 2.2, schemes 2 and 4, are F and 0 ion conductors, respectively, at high temperature. The 3 polymorph of 61303 has a fluorite-related structure with a large number of oxide vacancies. It has the highest oxide ion conductivity found to date at high temperatures, > 660 °C. 

The F -ion conductor first discovered by Faraday represents a more complex order-disorder transition to fast ionic conduction. At all temperatures, PbF2 is reported to have the fluorite structure in which the F ions occupy all the tetrahedral sites of a face-centred-cubic Pb -ion array however, the site potential of the Pb ions is asymmetric, and a measurement of the charge density with increasing temperature indicates that the F ions spend an increasing percentage of the time at the... 

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